Displaying similar documents to “The sharpness of convergence results for q -Bernstein polynomials in the case q > 1 ”

Approximation properties of bivariate complex q -Bernstein polynomials in the case q > 1

Nazim I. Mahmudov (2012)

Czechoslovak Mathematical Journal

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In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate q -Bernstein polynomials for a function analytic in the polydisc D R 1 × D R 2 = { z ∈ C : | z | < R 1 } × { z ∈ C : | z | < R 1 } for arbitrary fixed q > 1 . We give quantitative Voronovskaja type estimates for the bivariate q -Bernstein polynomials for q > 1 . In the univariate case the similar results were obtained by S. Ostrovska: q -Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255. and S. G. Gal: Approximation by Complex Bernstein...

The Lower Estimate for Bernstein Operator

Gal, Sorin G., Tachev, Gancho T. (2013)

Mathematica Balkanica New Series

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MSC 2010: 41A10, 41A15, 41A25, 41A36 For functions belonging to the classes C2[0; 1] and C3[0; 1], we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness. Several applications to some concrete examples of functions are presented.